Use a derivative to find the interval where the graph of y = x^4 - 7x is increasing. Any values should be in exact form.

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needs some help on how to do this exaclty thanks

mathlete

Since the derivative is the function that will tell you the slope of the line at any given point, it follows that if the derivative is positive at some point, then the slope is positive, and if the slope is positive the function is increasing.

So wherever the derivative is positive, the function is increasing.

If the function is continuous, then a function will be positive between zeros. Meaning it can only go from positive to negative or negative to positive if it touches the x-axis.

So what you need to do is first find the derivative so that you will know the function for the slope, then find the zeros of the derivative, then check points between them.

example: pretend the derivative is -x^2+4 (I just made this function up) then we solve for the zeroes, and get positive and negative 2. So the graph can (but doesn't always, which is why you need to test) change sign at these points. So we test x=-3, and get y=-5, we test x=0 and get y=4, we test x=3 and get y =-5. Then this means that all points prior to x=-2 will have a negative slope and be decreasing because the slope is negative, all points between x=-2 and x=2 will be increasing because the slope is positive, and all points after x=2 will be negative because the slope is positive.

So you can apply this same technique to your problem. Find the function of the slope (derivative) find the zeros of this function, test points around the zeros, check their signs, and positive signs will be increasing.